In an airborne or spaceborne SAR, microwaves illuminate the terrain below the platform, and the echoes scattered from the surface are collected. Subsequent signal processing performed on the echoes produces an image of the scene, where each picture element (pixel) contains amplitude and phase information. A display of the amplitude information produces the familiar SAR images, which look very similar to photographs with high spatial resolution, typically .about.10 m in a swath 50 km wide.
It has been demonstrated that interferometric SAR observations provide a means for obtaining high resolution topographic terrain maps from data acquired simultaneously at two slightly displaced antennas. R. M. Goldstein, E. R. Caro and C. Wu, U.S. Pat. No. 4,551,724 issued Nov. 5, 1987; H. A. Zebker and R. M. Goldstein, "Topographic Mapping from Interferometric Synthetic Aperture Radar Observations," Journal of Geophysical Research, Vol. 91, No. B5, pp. 4993-4999, (1986). Typically, topographic maps are produced from a stereo pair of optical photographs in which the appearance of the same terrain at slightly different positions is used to deduce the height of the terrain. That is distinct from the interferometric approach used in the present invention. The following is excerpted from the paper cited above.
In producing an interferometric SAR observation, two transversely spaced antennas A.sub.1 and A.sub.2 are mounted on an aircraft equipped with side-looking radar as shown in FIG. 1a. Reflected energy from the ground is received simultaneously by the two antennas and separately recorded and processed to yield two .about.10-m resolution complex images (magnitude and phase). The phase .phi. of the return signal from each resolution element (pixel) is maintained together with its magnitude. The two images are then combined pixel by pixel to obtain a single image with the phase of each pixel being the difference of the two original phases and the magnitude of each pixel the product of the two original magnitudes.
The radar system yields the line-of-sight distance (slant range) .rho. and .rho.' from each antenna to the target point P. The vertical distance h from the antenna to the surface is obtained from the solution of simple geometric relationships using either slant range. However, the slant range is indeterminate within the slant range resolution (typically .+-.3.75 m) of the radar which depends principally on the transmitted signal bandwidth. The interferometric technique permits determination of the slant range .rho.-.rho.' to much greater precision (typically 1 cm) as shown in FIG. 1b.
The two measurements of .rho. and .rho.', with the geometrical factors B and .theta. shown in FIG. 1b, are sufficient to find aircraft height h above each point in the radar image and from that deduce elevation of each point. The height h, when combined with the conventional along-track and slant-range (.rho.-.rho.') measurements, yields the three-dimensional position of a given point in the image. Knowledge of the location of each point then permits rectification of the image to a cartographically accurate form. In that manner, two SAR images recorded simultaneously with two receiving antennas separated slightly in the cross-track direction, or recorded with one antenna on two parallel but spaced apart passes, will provide topographic data of the terrain.
As just noted, it is possible to perform the necessary measurements for SAR interferometry with only one antenna mounted on one orbiting spacecraft, or on one or two aircraft, by making two passes over the terrain along separate but parallel paths. If the two passes are not parallel and instead are skewed, the difficulty of determining elevation of corresponding pixels in the separate images is substantially increased. A. K. Gabriel and R. M. Goldstein, "Crossed orbit interferometry: theory and experimental results from SIR-B," Int. J. Remote Sensing, Vol. 9, No. 5, pp. 857-872 (1988). In any case, it is recognized that in determining the elevation of any given point in the scene, the phase of the radar echoes may only be measured modulo 2.pi., whereas the whole phase N2.pi. is needed to determine absolute elevation. An approach to "unwrapping" the 2.pi. ambiguities in the data set has been presented in detail. R. M. Goldstein, H. A. Zebker and C. L. Werner, "Satellite radar interferometry: Two-dimensional phase unwrapping," Radio Science, Vol. 23, No. 4, pp. 713-720 (1988). The algorithm for deriving a satisfactory set of phases for SAR interferometry detailed there is incorporated here by reference.